Answer
a. $ -2i-2j$
b. $ 8i-13j$
c. $ -23$
d. $ 29$
Work Step by Step
Given $\vec v=2i-5j$ and $\vec w=-4i+3j$, we have
a. $\vec v + \vec w =(2-4)i + (-5+3)j=-2i-2j$
b. $2\vec v - \vec w =(4+4)i + (-10-3)j=8i-13j$
c. $\vec v\cdot \vec w =(2)(-4)+(-5)(3)=-23$
d. $\vec v\cdot \vec v =(2)(2)+(-5)(-5)=29$
